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Fourth-Order Numerical Scheme Based on Half-Step Non-Polynomial Spline Approximations for 1D Quasi-Linear Parabolic Equations

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ABSTRACT

In this article, we discuss a fourth-order accurate scheme based on non-polynomial splines in tension approximations for solving quasi-linear parabolic partial differential equations (PDEs). The proposed numerical method requires only two half-step points and a central point on a uniform mesh in spatial direction. This method is derived directly from the continuity condition for the first-order derivative of the non-polynomial tension spline function. The stability of the scheme is discussed using a model linear PDE. The method is applicable for solving singular parabolic problems in polar systems. The proposed method is tested on the generalized Burgers–Huxley equation, generalized Burgers–Fisher equation, and Burgers’ equations in polar coordinates.

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ACKNOWLEDGEMENTS

The authors would like to thank the reviewers for their valuable comments and remarks, which helped to improve the quality of the paper.

Funding

This work was supported by CSIR-SRF, grant no. 09/045(1161)/2012-EMR-I.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, South Asian University, 110021, New Delhi, India

    R. K. Mohanty

  2. Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, 110007, Delhi, India

    S. Sharma

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  1. R. K. Mohanty
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  2. S. Sharma
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Correspondence to R. K. Mohanty or S. Sharma.

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Mohanty, R.K., Sharma, S. Fourth-Order Numerical Scheme Based on Half-Step Non-Polynomial Spline Approximations for 1D Quasi-Linear Parabolic Equations. Numer. Analys. Appl. 13, 68–81 (2020). https://doi.org/10.1134/S1995423920010061

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  • DOI: https://doi.org/10.1134/S1995423920010061

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